On combining information from multiple gravitational wave sources

Aaron Zimmerman, Carl-Johan Haster, and Katerina Chatziioannou
Phys. Rev. D 99, 124044 – Published 25 June 2019

Abstract

In the coming years, advanced gravitational wave detectors will observe signals from a large number of compact binary coalescences. The majority of these signals will be relatively weak, making the precision measurement of subtle effects, such as deviations from general relativity, challenging in the individual events. However, many weak observations can be combined into precise inferences, if information from the individual signals is combined in an appropriate way. In this study we revisit common methods for combining multiple gravitational wave observations to test general relativity, namely (i) multiplying the individual likelihoods of beyond-general-relativity parameters and (ii) multiplying the Bayes factor in favor of general relativity from each event. We discuss both methods and show that they make stringent assumptions about the modified theory of gravity they test. In particular, the former assumes that all events share the same beyond-general-relativity parameter, while the latter assumes that the theory of gravity has a new unrelated parameter for each detection. We show that each method can fail to detect deviations from general relativity when the modified theory being tested violates these assumptions. We argue that these two methods are the extreme limits of a more generic framework of hierarchical inference on hyperparameters that characterize the underlying distribution of single-event parameters. We illustrate our conclusions first using a simple model of Gaussian likelihoods and also by applying parameter estimation techniques to a simulated dataset of gravitational waveforms in a model where the graviton is massive. We argue that combining information from multiple sources requires explicit assumptions that make the results inherently model dependent.

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  • Received 1 April 2019

DOI:https://doi.org/10.1103/PhysRevD.99.124044

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Aaron Zimmerman1,2, Carl-Johan Haster1,3,4, and Katerina Chatziioannou1,5

  • 1Canadian Institute for Theoretical Astrophysics, 60 St. George Street, Toronto, Ontario M5S 3H8, Canada
  • 2Theory Group, Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
  • 3LIGO Laboratory, Massachusetts Institute of Technology, 185 Albany Street, Cambridge, Massachusetts 02139, USA
  • 4MIT-Kavli Institute for Astrophysics and Space Research, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
  • 5Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA

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Issue

Vol. 99, Iss. 12 — 15 June 2019

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